This Grimtotem Spirit Guide here is probably the most beautiful pet in all of Azeroth -- which is all the more unfortunate because there's no longer any way to get him. During a very brief time just after Patch 2.3, hunters with lots of ingenuity and patience were able to use all kinds of special tricks in order to shorten their Tame Beast spell enough to catch this guy. At first, Blizzard said that they would allow us to continue taming these wolves, but very soon they changed their mind without warning and made them untamable. It was quite the fiasco, but at least some people got to have them -- if you were one of them, congratulations on having the most beautiful pet there is!
If you're looking for an alternative to the Grimtotem Spirit Guide, then the Ghost Saber will probably be your best bet. He's not quite the same as the ghost wolf, but he is transparent and ghostly looking. To tame him, you'll have to make your way up to the northernmost point of Darkshore, where you'll see a set of ruins with a bunch of naga loitering about. There, on the ground you should be able to find some Cat Figurines just laying about -- Keep trying to open them and eventually this ghostly cat will spawn, whereupon you may tame him. He'll be either level 19 or 20 when he spawns, so be sure that you are the appropriate level to tame him as well, and bring a throwaway pet to abandon as soon as you see him, just to make the fighting you have to do to find the figurines a bit less painful.
Speaking of kitties, the kitty you are most likely to have heard of is the Big Red Kitty, of so much infamous notoriety, and some of you may be wondering just what sort of kitty is the Big Red Kitty that BRK has named him after? The answer (I believe) is the Frostsaber Pride Watcher, found up in the far north of Winterspring, near Frostsaber Rock, and he looks just like the Wintersaber tigers the Alliance can learn to ride as an epic mount (if you have the patience for all the reputation you'll need first). He has a unique skin, (no other cat in the game is this shade of lavender), and he's not rare either -- you just waltz up and tame him at your leisure! While you're there, however, you might stumble upon the rare tiger Rak'shiri, who looks the same but with a slightly different color. Check him out and see which one you prefer.
Humar the Pridelord
If you're not superstitiously afraid of bad luck and a black cat is what you're after, then you can't go wrong with Humar the Pridelord, the black lion of the Barrens, a rare level 23 cat who spawns under a tree near Ratchet once every 8 to 12 hours or so. Getting him might require a bit of patience, but if you really like the look it'll be worth it to you. The commenters at Wowhead have left us a ton of great advice on how to make him yours, so if Humar's just your style, go have a look at some of their suggestions and choose which method of stalking your target is right for you.
What's up with all the cats, you ask? Well, they're the most popular pet in the game for a reason, and it isn't just because they do good damage. Their beauty has definitely played a role in their popularity, and some of the hard to get ones stand out a lot even from the run-of-the-mill normal cats you see all over the place. Echeykee is the only white lion in the game, and he's a level 16 beast summonable only through a Horde quest in the Barrens. If you're in the Alliance, you'll have to find a Horde friend to help you out on this one. [Edit: There's another white lion that I didn't know about in Winterspring, Sian-Rotam. Formerly Sian-Rotam was part of a Horde-only quest, but since patch 2.3, it is now open to the Alliance as well! Thanks to commenters for pointing this out to me.]
Loque'nahak here isn't exactly a cat, even though he may look like one. He's actually some sort of magical glowy spirit creature, and he's the only tamable Spirit Beast in the game. You'll be able to find him in Sholazar Basin, Northrend, but only if you're extremely lucky. He's a rare spawn who will be costantly camped by about 10 other hunters, round the clock, for the first month after the expansion is released, and possibly for a long time after that also. But that's not all -- he's also one of the objectives for the Northern Exposure achievement, so you'll also be running into other classes who are looking to strike him dead, possibly just while you are trying to tame him. Still... he is quite unique and quite beautiful, so to many of us out there, it'll be worth it to be so very extremely patient.
I've always loved owls, and have used one for most of my hunter career, starting with the grey one, replacing him with a white one, and finally graduating to the multi-colored owl of Skettis, in Terokkar Forest. In the Dragonblight region of Northrend, however, we'll be able to find the even more gorgeous Emerald Skytalon (level 73), who looks more like a jade statue than an actual living beast. As far as I can tell, he is the only tamable pet that seems to be made of stone rather than living flesh of some sort or another (with the possible exception of some core hounds).
These red dragonhawks from Eversong Forest have long been one of my favorite creatures in the game, but until recently, they were cursed with "caster stats," which lowered their effectiveness, especially at higher levels. Since patch 3.0.2, however, these caster stats have been removed, and they are now just as useful as any other dragonhawk you might find out there. If you're interested in the other color variations, have a look at the various dragonhawks available to you before settling on one.
Moths have long been the envy of most hunters, who saw them around various parts of Azeroth and Northrend and wished that they could be tamable, and now since patch 3.0.2, they are! All shades of moths are quite beautiful, but in the southern region of Borean Tundra, near Warsong Hold in Northrend, we'll be able to find a special white moth, called Aspatha the Broodmother, tameable at level 71. This one looks to me like the quintessence of mothiness, but not that ugly sort of eat-your-wardrobe type of mothiness, no -- this is the mothiness that makes moths so ethereal and wondrous!
Wind serpents have long been treasured as one of the most beautiful (and deadly) of pets available to hunters, and in Outland we were treated to some new and beautiful skins for them in various different colors. Now, in the Zul'Drak region of Northrend, we find a special white Scion of Quetz'lun, which has even more of that graceful and ethereal beauty to it. Still, if white isn't your favorite color, many other colors are just as beautiful.
Here we have the Sapphire Hive Queen, Big Red Kitty's favorite wasp, available only in Sholazar Basin, of Northrend. He's quite large, and quite ferocious looking, but still very attractive if you love really bright colors. As BRK put it, "He's got the colors of the rainbow, and he's like the LCD Acid Wasp of Doom!"
The Umbraglow Stinger (or its host of other variously colored wasps in Zangarmarsh) is quite the the cute little fella, who can follow you around wherever you go, and leave a cute little green trail of firefly light behind him. Big Red Kitty loves the little guy, so adorable!
Chimaeras aren't generally considered extremely beautiful pets, and Nuramoc here borders on the ugly with its sharp teeth sticking out in all directions. But there's something about the baby blue and pink colors on it which make it look as though it's more than just a toothy monster of death. It's like... the toothy monster of death that your toddler could ride around on for laughs, just as long as you were watching to see that the child didn't get eaten by mistake. If you want a chimaera for PvP, then this is your most attractive option. He's a rare spawn up in Netherstorm, however, so be prepared to wait and compete with other hunters for him.
Gorillas also aren't exactly the first creatures that come to your mind when you think of beautiful pets, but Uhk'loc here in the gorilla cave in northeastern Un'Goro Crater is a special one. He's the only albino gorilla in the game, possibly a tribute to the only known albino gorilla in real life, Snowflake, who died in 2003. He's level 52 or 53 rare spawn, however, so if you want him you'll have to be patient.
Finally, rounding out our list of the most beautiful pets you can tame is the Kurken, who, unlike most other core hounds, does not drip molten saliva or fume with sulfuric stench. Quite the opposite, in spite of his sharp fangs and glowing red eyes, he actually looks kind of cuddly when you're not looking straight up into his gaping jaws. His back glows with a pretty white cloud too, which makes him quite the looker. You can find him most any time at level 12 in the northernmost cave of Azuremyst Isle, Stillpine Hold.